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Block #860,980

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/20/2014, 4:12:57 PM Β· Difficulty 10.9640 Β· 5,949,691 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
3fa0641ddbf8bd18eba19c53472389528a976ca0fb07a6567fcc8cb60cdc0e62
View on Chainz β†—

Height

#860,980

Difficulty

10.964014

Transactions

2

Size

729 B

Version

2

Bits

0af6c99f

Nonce

1,169,661,860

Timestamp

12/20/2014, 4:12:57 PM

Confirmations

5,949,691

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

24ec401f2fa6a31613319e157d20bed41155bdf9a05c94e9daa40c029ea15c40
Transactions (2)
Coinbase83d834ae01862a…4d12853bfc2621
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
5d71cce85e9823…5eb9b25a09384c
3 in β†’ 2 out17178.3360 XPM523 B
AU5vyncw…j3vqEh9gAe9RpSR4…EXdTFp6s
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.723 Γ— 10⁹⁴(95-digit number)
17232078265594924063…08192248039690396999
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.723 Γ— 10⁹⁴(95-digit number)
17232078265594924063…08192248039690396999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.723 Γ— 10⁹⁴(95-digit number)
17232078265594924063…08192248039690397001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
3.446 Γ— 10⁹⁴(95-digit number)
34464156531189848127…16384496079380793999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.446 Γ— 10⁹⁴(95-digit number)
34464156531189848127…16384496079380794001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
6.892 Γ— 10⁹⁴(95-digit number)
68928313062379696255…32768992158761587999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.892 Γ— 10⁹⁴(95-digit number)
68928313062379696255…32768992158761588001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.378 Γ— 10⁹⁡(96-digit number)
13785662612475939251…65537984317523175999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.378 Γ— 10⁹⁡(96-digit number)
13785662612475939251…65537984317523176001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.757 Γ— 10⁹⁡(96-digit number)
27571325224951878502…31075968635046351999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.757 Γ— 10⁹⁡(96-digit number)
27571325224951878502…31075968635046352001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
5.514 Γ— 10⁹⁡(96-digit number)
55142650449903757004…62151937270092703999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,729,459 XPMΒ·at block #6,810,670 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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