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Block #531,968

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/8/2014, 7:49:27 PM Β· Difficulty 10.8958 Β· 6,277,814 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5226e07c3eabd6e5605bd43befbef5ad868627bfc385b299e9c32317f22f0acc
View on Chainz β†—

Height

#531,968

Difficulty

10.895803

Transactions

1

Size

208 B

Version

2

Bits

0ae55357

Nonce

68,525,315

Timestamp

5/8/2014, 7:49:27 PM

Confirmations

6,277,814

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c1b942b1a7b81ea8ca14fc13d7049c1dbba6f06322f985290d9af0a664c264c1
Transactions (1)
Coinbasec1b942b1a7b81e…9af0a664c264c1
1 in β†’ 1 out8.4100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.426 Γ— 10¹⁰⁰(101-digit number)
14264403642365149193…54985737100682559999
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
1.426 Γ— 10¹⁰⁰(101-digit number)
14264403642365149193…54985737100682559999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.426 Γ— 10¹⁰⁰(101-digit number)
14264403642365149193…54985737100682560001
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
2.852 Γ— 10¹⁰⁰(101-digit number)
28528807284730298387…09971474201365119999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.852 Γ— 10¹⁰⁰(101-digit number)
28528807284730298387…09971474201365120001
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
5.705 Γ— 10¹⁰⁰(101-digit number)
57057614569460596774…19942948402730239999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.705 Γ— 10¹⁰⁰(101-digit number)
57057614569460596774…19942948402730240001
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
1.141 Γ— 10¹⁰¹(102-digit number)
11411522913892119354…39885896805460479999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.141 Γ— 10¹⁰¹(102-digit number)
11411522913892119354…39885896805460480001
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
2.282 Γ— 10¹⁰¹(102-digit number)
22823045827784238709…79771793610920959999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.282 Γ— 10¹⁰¹(102-digit number)
22823045827784238709…79771793610920960001
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:57,722,335 XPMΒ·at block #6,809,781 Β· updates every 60s
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