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Block #860,734

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/20/2014, 12:03:07 PM Β· Difficulty 10.9640 Β· 5,957,204 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
27a1bb220add05e34d02b9ef19335770f4f4da666d36be74125a2f88b40d4972
View on Chainz β†—

Height

#860,734

Difficulty

10.964038

Transactions

2

Size

581 B

Version

2

Bits

0af6cb2f

Nonce

123,539,230

Timestamp

12/20/2014, 12:03:07 PM

Confirmations

5,957,204

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3f538989842db50c03029c1accb47f0e9aeb6d0be613c28fe5cedd7de034ae8f
Transactions (2)
Coinbasecdbeff7efc5f26…7b67d166156f18
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
ec134cf9581be2…b2ecadee221dbb
2 in β†’ 2 out686.0800 XPM374 B
AahsA3Tq…ZNc46vZTAGkH55Vp…kSi9QpTD
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.

1.770 Γ— 10⁹⁷(98-digit number)
17705350253722796227…96488851863539532799
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
1.770 Γ— 10⁹⁷(98-digit number)
17705350253722796227…96488851863539532799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.770 Γ— 10⁹⁷(98-digit number)
17705350253722796227…96488851863539532801
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
3.541 Γ— 10⁹⁷(98-digit number)
35410700507445592455…92977703727079065599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.541 Γ— 10⁹⁷(98-digit number)
35410700507445592455…92977703727079065601
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
7.082 Γ— 10⁹⁷(98-digit number)
70821401014891184910…85955407454158131199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.082 Γ— 10⁹⁷(98-digit number)
70821401014891184910…85955407454158131201
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
1.416 Γ— 10⁹⁸(99-digit number)
14164280202978236982…71910814908316262399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.416 Γ— 10⁹⁸(99-digit number)
14164280202978236982…71910814908316262401
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
2.832 Γ— 10⁹⁸(99-digit number)
28328560405956473964…43821629816632524799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.832 Γ— 10⁹⁸(99-digit number)
28328560405956473964…43821629816632524801
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
5.665 Γ— 10⁹⁸(99-digit number)
56657120811912947928…87643259633265049599
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:57,787,569 XPMΒ·at block #6,817,937 Β· updates every 60s
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