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Block #531,133

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/8/2014, 7:46:33 AM Β· Difficulty 10.8934 Β· 6,272,284 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cd6bb70f2b1d619e536bfe9a2dd73f3a4ad06fcd5a742d34c7054aa72ad7f38c
View on Chainz β†—

Height

#531,133

Difficulty

10.893448

Transactions

3

Size

959 B

Version

2

Bits

0ae4b909

Nonce

51,654,602

Timestamp

5/8/2014, 7:46:33 AM

Confirmations

6,272,284

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

36f2611ae63ca59f1e774b2ae634f558b9413f5a17b9bca78e4bf8c6bbf38a00
Transactions (3)
Coinbase7350d04ebd6522…7c8750a656dbeb
1 in β†’ 1 out8.4300 XPM116 B
ANSXnLY2…Sd25TjkD
492e28fdd49956…4b712438c0809b
3 in β†’ 2 out25.3300 XPM525 B
AQ6HeNTK…jgwW2QVzAaUNi76B…wtcm5mLM
fe81665d63802f…d3f702cbf44092
1 in β†’ 2 out1.3473 XPM226 B
AZUm9GX6…tZ5dn1V6AdGaEuE4…4fB5D786
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.

8.424 Γ— 10⁹⁸(99-digit number)
84249164084192623718…99854763016835984559
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
8.424 Γ— 10⁹⁸(99-digit number)
84249164084192623718…99854763016835984559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.424 Γ— 10⁹⁸(99-digit number)
84249164084192623718…99854763016835984561
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
1.684 Γ— 10⁹⁹(100-digit number)
16849832816838524743…99709526033671969119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.684 Γ— 10⁹⁹(100-digit number)
16849832816838524743…99709526033671969121
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
3.369 Γ— 10⁹⁹(100-digit number)
33699665633677049487…99419052067343938239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.369 Γ— 10⁹⁹(100-digit number)
33699665633677049487…99419052067343938241
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
6.739 Γ— 10⁹⁹(100-digit number)
67399331267354098974…98838104134687876479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.739 Γ— 10⁹⁹(100-digit number)
67399331267354098974…98838104134687876481
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
1.347 Γ— 10¹⁰⁰(101-digit number)
13479866253470819794…97676208269375752959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.347 Γ— 10¹⁰⁰(101-digit number)
13479866253470819794…97676208269375752961
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:57,671,367 XPMΒ·at block #6,803,416 Β· updates every 60s
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