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Block #190,107

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/2/2013, 6:36:21 AM Β· Difficulty 9.8737 Β· 6,615,671 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b6a74415edf22ea9e77cfda74b2c2660eb327f09a248cb352fa3ac45a8842bf8
View on Chainz β†—

Height

#190,107

Difficulty

9.873715

Transactions

1

Size

198 B

Version

2

Bits

09dfabd1

Nonce

192,677

Timestamp

10/2/2013, 6:36:21 AM

Confirmations

6,615,671

Mined by

⛏️ P2SHARBvr1evuYzdjmXQBMTxCmA4hCNg7YPkPH

Merkle Root

afe5cef6b705cadbe7a188dc2ba33bf3de946580b23b8655f8ef22f16bc93308
Transactions (1)
Coinbaseafe5cef6b705ca…ef22f16bc93308
1 in β†’ 1 out10.2400 XPM109 B
ARBvr1ev…Ng7YPkPH
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.

6.628 Γ— 10⁹²(93-digit number)
66286723525282526591…07654834569818434559
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
6.628 Γ— 10⁹²(93-digit number)
66286723525282526591…07654834569818434559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.628 Γ— 10⁹²(93-digit number)
66286723525282526591…07654834569818434561
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
1.325 Γ— 10⁹³(94-digit number)
13257344705056505318…15309669139636869119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.325 Γ— 10⁹³(94-digit number)
13257344705056505318…15309669139636869121
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
2.651 Γ— 10⁹³(94-digit number)
26514689410113010636…30619338279273738239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.651 Γ— 10⁹³(94-digit number)
26514689410113010636…30619338279273738241
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
5.302 Γ— 10⁹³(94-digit number)
53029378820226021273…61238676558547476479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.302 Γ— 10⁹³(94-digit number)
53029378820226021273…61238676558547476481
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
1.060 Γ— 10⁹⁴(95-digit number)
10605875764045204254…22477353117094952959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.060 Γ— 10⁹⁴(95-digit number)
10605875764045204254…22477353117094952961
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:57,690,310 XPMΒ·at block #6,805,777 Β· updates every 60s
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