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Block #38,164

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 11:39:01 AM Β· Difficulty 8.1421 Β· 6,756,790 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
907aec6dfa1e3d7e66169bf277c828869819d0240640841d8cd88d5c2150eab1
View on Chainz β†—

Height

#38,164

Difficulty

8.142104

Transactions

1

Size

201 B

Version

2

Bits

082460f2

Nonce

699

Timestamp

7/14/2013, 11:39:01 AM

Confirmations

6,756,790

Mined by

⛏️ P2SHAQi5QmwpsL7hvDVWrJmtdKwdxsh7qfQEQF

Merkle Root

91ddea4a2bda08fad4165fa520407b62dbc62c1f8d7f467bf6437d51509d49bc
Transactions (1)
Coinbase91ddea4a2bda08…437d51509d49bc
1 in β†’ 1 out15.0600 XPM110 B
AQi5Qmwp…h7qfQEQF
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.

1.010 Γ— 10⁹⁸(99-digit number)
10101649837865763224…54613614751283967359
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
1.010 Γ— 10⁹⁸(99-digit number)
10101649837865763224…54613614751283967359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.010 Γ— 10⁹⁸(99-digit number)
10101649837865763224…54613614751283967361
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
2.020 Γ— 10⁹⁸(99-digit number)
20203299675731526449…09227229502567934719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.020 Γ— 10⁹⁸(99-digit number)
20203299675731526449…09227229502567934721
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
4.040 Γ— 10⁹⁸(99-digit number)
40406599351463052899…18454459005135869439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.040 Γ— 10⁹⁸(99-digit number)
40406599351463052899…18454459005135869441
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
8.081 Γ— 10⁹⁸(99-digit number)
80813198702926105799…36908918010271738879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.081 Γ— 10⁹⁸(99-digit number)
80813198702926105799…36908918010271738881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,603,668 XPMΒ·at block #6,794,953 Β· updates every 60s
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