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Block #223,862

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/23/2013, 8:34:53 AM Β· Difficulty 9.9374 Β· 6,572,583 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4cb22f6b640c5c1ec5cf2a6bb362fdc7c1becb6689b79aaf378ac9f923d4a401
View on Chainz β†—

Height

#223,862

Difficulty

9.937410

Transactions

2

Size

720 B

Version

2

Bits

09effa1b

Nonce

201,988

Timestamp

10/23/2013, 8:34:53 AM

Confirmations

6,572,583

Mined by

⛏️ P2SHAefNmfCCiMUgcSMoZqwmWZgc6ARj9JS3UM

Merkle Root

4a5f5875e0e74f971fbeee527349994ec880b1a203b39f2c31e79860edf8a042
Transactions (2)
Coinbasec2684437612b4b…054b416b9930dd
1 in β†’ 1 out10.1200 XPM109 B
AefNmfCC…Rj9JS3UM
d2784509db577b…4e310a6b185040
3 in β†’ 2 out15.3759 XPM521 B
Ae5f4FYC…CMTtsLJDAZy8rAg6…DSSL4AkK
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.

1.766 Γ— 10⁹⁴(95-digit number)
17666661332056051874…98952589063193179359
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
1.766 Γ— 10⁹⁴(95-digit number)
17666661332056051874…98952589063193179359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.766 Γ— 10⁹⁴(95-digit number)
17666661332056051874…98952589063193179361
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
3.533 Γ— 10⁹⁴(95-digit number)
35333322664112103749…97905178126386358719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.533 Γ— 10⁹⁴(95-digit number)
35333322664112103749…97905178126386358721
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
7.066 Γ— 10⁹⁴(95-digit number)
70666645328224207499…95810356252772717439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.066 Γ— 10⁹⁴(95-digit number)
70666645328224207499…95810356252772717441
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
1.413 Γ— 10⁹⁡(96-digit number)
14133329065644841499…91620712505545434879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.413 Γ— 10⁹⁡(96-digit number)
14133329065644841499…91620712505545434881
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
2.826 Γ— 10⁹⁡(96-digit number)
28266658131289682999…83241425011090869759
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:57,615,553 XPMΒ·at block #6,796,444 Β· updates every 60s
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