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Block #231,930

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/28/2013, 6:49:48 PM Β· Difficulty 9.9408 Β· 6,563,733 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b774556afa844d141f541a791b1ed03102aae1b7c0e7852f1fac255b6dde00a0
View on Chainz β†—

Height

#231,930

Difficulty

9.940804

Transactions

1

Size

198 B

Version

2

Bits

09f0d88f

Nonce

50,877

Timestamp

10/28/2013, 6:49:48 PM

Confirmations

6,563,733

Mined by

⛏️ P2SHAHPLSWVdVVmfZ1Mw8oxTBdXzN3ZdicvSUu

Merkle Root

cb6820da6996426a840918f8be4e1830e3b853bfbbf4d758faf15df832993e94
Transactions (1)
Coinbasecb6820da699642…f15df832993e94
1 in β†’ 1 out10.1000 XPM109 B
AHPLSWVd…ZdicvSUu
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.

1.201 Γ— 10⁹³(94-digit number)
12013776224809962157…02783617666989317549
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
1.201 Γ— 10⁹³(94-digit number)
12013776224809962157…02783617666989317549
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.201 Γ— 10⁹³(94-digit number)
12013776224809962157…02783617666989317551
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
2.402 Γ— 10⁹³(94-digit number)
24027552449619924315…05567235333978635099
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.402 Γ— 10⁹³(94-digit number)
24027552449619924315…05567235333978635101
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
4.805 Γ— 10⁹³(94-digit number)
48055104899239848630…11134470667957270199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.805 Γ— 10⁹³(94-digit number)
48055104899239848630…11134470667957270201
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
9.611 Γ— 10⁹³(94-digit number)
96110209798479697261…22268941335914540399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.611 Γ— 10⁹³(94-digit number)
96110209798479697261…22268941335914540401
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
1.922 Γ— 10⁹⁴(95-digit number)
19222041959695939452…44537882671829080799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.922 Γ— 10⁹⁴(95-digit number)
19222041959695939452…44537882671829080801
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:57,609,376 XPMΒ·at block #6,795,662 Β· updates every 60s
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