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Block #173,786

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/21/2013, 6:09:37 AM Β· Difficulty 9.8598 Β· 6,668,599 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
82ec25c63f321ae198db66823f6691990a2b303ab9e15493d4314f85b85bd410
View on Chainz β†—

Height

#173,786

Difficulty

9.859752

Transactions

1

Size

198 B

Version

2

Bits

09dc18b2

Nonce

3,140

Timestamp

9/21/2013, 6:09:37 AM

Confirmations

6,668,599

Mined by

⛏️ P2SHAUmDUZFkSaTxaa2LqVTkrDNDJBCVC4xpC8

Merkle Root

e0ddafbc4c5b868aca8c3675802719df98bb7536ed6f9e01dedb2ebd7d488613
Transactions (1)
Coinbasee0ddafbc4c5b86…db2ebd7d488613
1 in β†’ 1 out10.2700 XPM109 B
AUmDUZFk…CVC4xpC8
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.

1.538 Γ— 10⁹²(93-digit number)
15389147763922865157…22976096127474706759
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
1.538 Γ— 10⁹²(93-digit number)
15389147763922865157…22976096127474706759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.538 Γ— 10⁹²(93-digit number)
15389147763922865157…22976096127474706761
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
3.077 Γ— 10⁹²(93-digit number)
30778295527845730315…45952192254949413519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.077 Γ— 10⁹²(93-digit number)
30778295527845730315…45952192254949413521
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
6.155 Γ— 10⁹²(93-digit number)
61556591055691460630…91904384509898827039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.155 Γ— 10⁹²(93-digit number)
61556591055691460630…91904384509898827041
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
1.231 Γ— 10⁹³(94-digit number)
12311318211138292126…83808769019797654079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.231 Γ— 10⁹³(94-digit number)
12311318211138292126…83808769019797654081
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
2.462 Γ— 10⁹³(94-digit number)
24622636422276584252…67617538039595308159
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:57,983,489 XPMΒ·at block #6,842,384 Β· updates every 60s
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