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Block #1,060,664

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/15/2015, 4:23:26 PM Β· Difficulty 10.7279 Β· 5,747,256 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f8fb4166c5b207af9d73e08ea9ff1e79e46fa688a04e7acbca477a4bcc23bb8b
View on Chainz β†—

Height

#1,060,664

Difficulty

10.727946

Transactions

2

Size

1.00 KB

Version

2

Bits

0aba5ab2

Nonce

664,200,063

Timestamp

5/15/2015, 4:23:26 PM

Confirmations

5,747,256

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

07f3663de9ffdc186cb9cb3de096119816d3acc610f24141127e12b91a56f417
Transactions (2)
Coinbase43a1ae76d9a06b…43620b9930f8eb
1 in β†’ 1 out8.6900 XPM116 B
ANSXnLY2…Sd25TjkD
f8af116afd5720…8ab56f672a4bd0
5 in β†’ 2 out10.0201 XPM819 B
Ae9drWdk…FnLTm9PnAZA1QNdM…JgP3ZVnr
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.

1.985 Γ— 10⁹⁡(96-digit number)
19855928667903221018…78026146802450467979
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
1.985 Γ— 10⁹⁡(96-digit number)
19855928667903221018…78026146802450467979
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.985 Γ— 10⁹⁡(96-digit number)
19855928667903221018…78026146802450467981
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
3.971 Γ— 10⁹⁡(96-digit number)
39711857335806442037…56052293604900935959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.971 Γ— 10⁹⁡(96-digit number)
39711857335806442037…56052293604900935961
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
7.942 Γ— 10⁹⁡(96-digit number)
79423714671612884075…12104587209801871919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.942 Γ— 10⁹⁡(96-digit number)
79423714671612884075…12104587209801871921
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
1.588 Γ— 10⁹⁢(97-digit number)
15884742934322576815…24209174419603743839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.588 Γ— 10⁹⁢(97-digit number)
15884742934322576815…24209174419603743841
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
3.176 Γ— 10⁹⁢(97-digit number)
31769485868645153630…48418348839207487679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.176 Γ— 10⁹⁢(97-digit number)
31769485868645153630…48418348839207487681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,707,395 XPMΒ·at block #6,807,919 Β· updates every 60s
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