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Block #249,599

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/8/2013, 1:26:06 AM Β· Difficulty 9.9671 Β· 6,567,157 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
509e41af983358ee88515bf43dd743821d767870f2a8e3aa89c55d4e795f1b83
View on Chainz β†—

Height

#249,599

Difficulty

9.967083

Transactions

1

Size

199 B

Version

2

Bits

09f792c2

Nonce

25,619

Timestamp

11/8/2013, 1:26:06 AM

Confirmations

6,567,157

Mined by

⛏️ P2SHAHuUFvcwFs1vESjXtQLYzFAMgcYLgfEVC7

Merkle Root

214bb8b28afd81117819b5693e129f2e828b1b2f835ca7e0e031eb9c91e70b23
Transactions (1)
Coinbase214bb8b28afd81…31eb9c91e70b23
1 in β†’ 1 out10.0500 XPM109 B
AHuUFvcw…YLgfEVC7
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.

1.847 Γ— 10⁹⁡(96-digit number)
18471220780564294304…46057383062428047359
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
1.847 Γ— 10⁹⁡(96-digit number)
18471220780564294304…46057383062428047359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.847 Γ— 10⁹⁡(96-digit number)
18471220780564294304…46057383062428047361
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
3.694 Γ— 10⁹⁡(96-digit number)
36942441561128588608…92114766124856094719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.694 Γ— 10⁹⁡(96-digit number)
36942441561128588608…92114766124856094721
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
7.388 Γ— 10⁹⁡(96-digit number)
73884883122257177216…84229532249712189439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.388 Γ— 10⁹⁡(96-digit number)
73884883122257177216…84229532249712189441
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
1.477 Γ— 10⁹⁢(97-digit number)
14776976624451435443…68459064499424378879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.477 Γ— 10⁹⁢(97-digit number)
14776976624451435443…68459064499424378881
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
2.955 Γ— 10⁹⁢(97-digit number)
29553953248902870886…36918128998848757759
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:57,778,079 XPMΒ·at block #6,816,755 Β· updates every 60s
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