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Block #122,229

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/18/2013, 8:53:34 AM Β· Difficulty 9.7538 Β· 6,690,406 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e170bc8278cbdf7edbe14bc24e26e678f86b72456bc48e14518af40c2aef71bb
View on Chainz β†—

Height

#122,229

Difficulty

9.753850

Transactions

1

Size

200 B

Version

2

Bits

09c0fc4e

Nonce

228,934

Timestamp

8/18/2013, 8:53:34 AM

Confirmations

6,690,406

Mined by

⛏️ P2SHAZeU2g2L3DVc23NKBGDPLkL6PBm694WpGV

Merkle Root

77abd5abe25070ef1505a738c4deb146e269cc62f9aa9b01cfcdcda68ecb70bb
Transactions (1)
Coinbase77abd5abe25070…cdcda68ecb70bb
1 in β†’ 1 out10.5000 XPM109 B
AZeU2g2L…m694WpGV
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.

1.153 Γ— 10⁹⁸(99-digit number)
11539754949001178813…28589356352211098669
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
1.153 Γ— 10⁹⁸(99-digit number)
11539754949001178813…28589356352211098669
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.153 Γ— 10⁹⁸(99-digit number)
11539754949001178813…28589356352211098671
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
2.307 Γ— 10⁹⁸(99-digit number)
23079509898002357627…57178712704422197339
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.307 Γ— 10⁹⁸(99-digit number)
23079509898002357627…57178712704422197341
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
4.615 Γ— 10⁹⁸(99-digit number)
46159019796004715254…14357425408844394679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.615 Γ— 10⁹⁸(99-digit number)
46159019796004715254…14357425408844394681
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
9.231 Γ— 10⁹⁸(99-digit number)
92318039592009430509…28714850817688789359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.231 Γ— 10⁹⁸(99-digit number)
92318039592009430509…28714850817688789361
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
1.846 Γ— 10⁹⁹(100-digit number)
18463607918401886101…57429701635377578719
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:57,745,116 XPMΒ·at block #6,812,634 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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