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Block #309,717

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/13/2013, 5:49:32 PM Β· Difficulty 9.9949 Β· 6,485,238 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ff696b887ff90c5c390a94f29fdcb67a8a7ff7cf4bb6d19afa4030df5a35c29e
View on Chainz β†—

Height

#309,717

Difficulty

9.994928

Transactions

2

Size

1015 B

Version

2

Bits

09feb3a2

Nonce

63,227

Timestamp

12/13/2013, 5:49:32 PM

Confirmations

6,485,238

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

960a98e714c3a7c47dfe622f804d84f9395a2eb6838c2b0061aa77d62e151d90
Transactions (2)
Coinbase44788d097e2128…f446864c2f1800
1 in β†’ 1 out10.0100 XPM110 B
AeKNrjNj…1NEq95Ta
f99c84aa501024…e0ae852768df32
5 in β†’ 2 out1053.5100 XPM817 B
AHBzhBZd…H32uf4DkAHfCX7xS…5LyCD7mr
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.

1.013 Γ— 10⁸⁹(90-digit number)
10131868830844463551…32862116757810426979
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
1.013 Γ— 10⁸⁹(90-digit number)
10131868830844463551…32862116757810426979
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.013 Γ— 10⁸⁹(90-digit number)
10131868830844463551…32862116757810426981
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
2.026 Γ— 10⁸⁹(90-digit number)
20263737661688927103…65724233515620853959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.026 Γ— 10⁸⁹(90-digit number)
20263737661688927103…65724233515620853961
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
4.052 Γ— 10⁸⁹(90-digit number)
40527475323377854206…31448467031241707919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.052 Γ— 10⁸⁹(90-digit number)
40527475323377854206…31448467031241707921
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
8.105 Γ— 10⁸⁹(90-digit number)
81054950646755708412…62896934062483415839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.105 Γ— 10⁸⁹(90-digit number)
81054950646755708412…62896934062483415841
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
1.621 Γ— 10⁹⁰(91-digit number)
16210990129351141682…25793868124966831679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.621 Γ— 10⁹⁰(91-digit number)
16210990129351141682…25793868124966831681
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:57,603,677 XPMΒ·at block #6,794,954 Β· updates every 60s
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