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Block #247,445

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/6/2013, 6:57:33 PM Β· Difficulty 9.9648 Β· 6,563,471 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d2bb46f213259174b55c42f35193a28617cf755d8071faf3c7e8ad7c069ba65d
View on Chainz β†—

Height

#247,445

Difficulty

9.964801

Transactions

1

Size

199 B

Version

2

Bits

09f6fd34

Nonce

18,775

Timestamp

11/6/2013, 6:57:33 PM

Confirmations

6,563,471

Mined by

⛏️ P2SHAX7gbCESWBdicXagn4tivgB5CGHCFkaYNg

Merkle Root

3dfb1a1dfc1928eed785cb24f356ec4d2abd9a06839cbd73cac066557448e123
Transactions (1)
Coinbase3dfb1a1dfc1928…c066557448e123
1 in β†’ 1 out10.0600 XPM109 B
AX7gbCES…HCFkaYNg
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.

5.345 Γ— 10⁹³(94-digit number)
53458975625761097312…33144078402522282279
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
5.345 Γ— 10⁹³(94-digit number)
53458975625761097312…33144078402522282279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.345 Γ— 10⁹³(94-digit number)
53458975625761097312…33144078402522282281
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
1.069 Γ— 10⁹⁴(95-digit number)
10691795125152219462…66288156805044564559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.069 Γ— 10⁹⁴(95-digit number)
10691795125152219462…66288156805044564561
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
2.138 Γ— 10⁹⁴(95-digit number)
21383590250304438924…32576313610089129119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.138 Γ— 10⁹⁴(95-digit number)
21383590250304438924…32576313610089129121
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
4.276 Γ— 10⁹⁴(95-digit number)
42767180500608877849…65152627220178258239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.276 Γ— 10⁹⁴(95-digit number)
42767180500608877849…65152627220178258241
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
8.553 Γ— 10⁹⁴(95-digit number)
85534361001217755699…30305254440356516479
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:57,731,429 XPMΒ·at block #6,810,915 Β· updates every 60s
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