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Block #218,594

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/20/2013, 12:57:35 AM Β· Difficulty 9.9308 Β· 6,597,712 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5f97b5fbb60b1be05951f97bc1c212647bea0c425083c47d029abf9e5f823600
View on Chainz β†—

Height

#218,594

Difficulty

9.930772

Transactions

1

Size

200 B

Version

2

Bits

09ee4716

Nonce

191,441

Timestamp

10/20/2013, 12:57:35 AM

Confirmations

6,597,712

Mined by

⛏️ P2SHATRnMoWiPfLU4bA2TUCHsxS8iKZP2o2dcV

Merkle Root

821c894ee0de3a85c7914951cd73d9f4f389578bf49e722b679fd3f03d5da8d2
Transactions (1)
Coinbase821c894ee0de3a…9fd3f03d5da8d2
1 in β†’ 1 out10.1200 XPM109 B
ATRnMoWi…ZP2o2dcV
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.

2.881 Γ— 10⁹⁢(97-digit number)
28810279274147713800…08288674385795007039
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
2.881 Γ— 10⁹⁢(97-digit number)
28810279274147713800…08288674385795007039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.881 Γ— 10⁹⁢(97-digit number)
28810279274147713800…08288674385795007041
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
5.762 Γ— 10⁹⁢(97-digit number)
57620558548295427601…16577348771590014079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.762 Γ— 10⁹⁢(97-digit number)
57620558548295427601…16577348771590014081
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
1.152 Γ— 10⁹⁷(98-digit number)
11524111709659085520…33154697543180028159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.152 Γ— 10⁹⁷(98-digit number)
11524111709659085520…33154697543180028161
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
2.304 Γ— 10⁹⁷(98-digit number)
23048223419318171040…66309395086360056319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.304 Γ— 10⁹⁷(98-digit number)
23048223419318171040…66309395086360056321
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
4.609 Γ— 10⁹⁷(98-digit number)
46096446838636342081…32618790172720112639
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:57,774,568 XPMΒ·at block #6,816,305 Β· updates every 60s
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