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Block #138,182

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2013, 6:34:02 AM Β· Difficulty 9.8246 Β· 6,656,867 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
376401f43c486299275e0890999f1442085a67e672097f1d72470900df09aa03
View on Chainz β†—

Height

#138,182

Difficulty

9.824577

Transactions

1

Size

198 B

Version

2

Bits

09d3177f

Nonce

276,472

Timestamp

8/28/2013, 6:34:02 AM

Confirmations

6,656,867

Mined by

⛏️ P2SHAJGsd2f2XBU5XZ2GBxk9dj2VeiLh4yK7jj

Merkle Root

6e393888f84dbafefdb05c9aadab17c7dd74807f24e4e9e0f0df852f32443bb4
Transactions (1)
Coinbase6e393888f84dba…df852f32443bb4
1 in β†’ 1 out10.3400 XPM109 B
AJGsd2f2…Lh4yK7jj
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.

1.756 Γ— 10⁹³(94-digit number)
17561301489337454137…93207093798714938559
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
1.756 Γ— 10⁹³(94-digit number)
17561301489337454137…93207093798714938559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.756 Γ— 10⁹³(94-digit number)
17561301489337454137…93207093798714938561
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
3.512 Γ— 10⁹³(94-digit number)
35122602978674908274…86414187597429877119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.512 Γ— 10⁹³(94-digit number)
35122602978674908274…86414187597429877121
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
7.024 Γ— 10⁹³(94-digit number)
70245205957349816548…72828375194859754239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.024 Γ— 10⁹³(94-digit number)
70245205957349816548…72828375194859754241
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
1.404 Γ— 10⁹⁴(95-digit number)
14049041191469963309…45656750389719508479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.404 Γ— 10⁹⁴(95-digit number)
14049041191469963309…45656750389719508481
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
2.809 Γ— 10⁹⁴(95-digit number)
28098082382939926619…91313500779439016959
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9

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:57,604,432 XPMΒ·at block #6,795,048 Β· updates every 60s
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