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Block #199,568

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/8/2013, 11:14:41 AM Β· Difficulty 9.8878 Β· 6,626,753 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7c2ad14293800b08a1c93a7008c4e1179e2a4fcc003bb72e8a80582b67d45d85
View on Chainz β†—

Height

#199,568

Difficulty

9.887756

Transactions

1

Size

199 B

Version

2

Bits

09e343fc

Nonce

11,407

Timestamp

10/8/2013, 11:14:41 AM

Confirmations

6,626,753

Mined by

⛏️ P2SHAbGZZ5j9xYn1T2NM8sUHpoY2ocPsAgN9dv

Merkle Root

2970cf2ba989b169d32e4008c52b6a0b87691685b611439fe1be26a07cb87f4f
Transactions (1)
Coinbase2970cf2ba989b1…be26a07cb87f4f
1 in β†’ 1 out10.2100 XPM109 B
AbGZZ5j9…PsAgN9dv
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.

3.084 Γ— 10⁹³(94-digit number)
30845686567638094471…69894129118198288719
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
3.084 Γ— 10⁹³(94-digit number)
30845686567638094471…69894129118198288719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.084 Γ— 10⁹³(94-digit number)
30845686567638094471…69894129118198288721
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
6.169 Γ— 10⁹³(94-digit number)
61691373135276188942…39788258236396577439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.169 Γ— 10⁹³(94-digit number)
61691373135276188942…39788258236396577441
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
1.233 Γ— 10⁹⁴(95-digit number)
12338274627055237788…79576516472793154879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.233 Γ— 10⁹⁴(95-digit number)
12338274627055237788…79576516472793154881
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
2.467 Γ— 10⁹⁴(95-digit number)
24676549254110475577…59153032945586309759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.467 Γ— 10⁹⁴(95-digit number)
24676549254110475577…59153032945586309761
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
4.935 Γ— 10⁹⁴(95-digit number)
49353098508220951154…18306065891172619519
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:57,854,708 XPMΒ·at block #6,826,320 Β· updates every 60s
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