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Block #223,561

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/23/2013, 3:02:05 AM Β· Difficulty 9.9378 Β· 6,582,251 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0b759c06bb6368dfece23c4509db006687cdcaec58f11a0114b4e759faf7121c
View on Chainz β†—

Height

#223,561

Difficulty

9.937768

Transactions

1

Size

198 B

Version

2

Bits

09f01196

Nonce

78,728

Timestamp

10/23/2013, 3:02:05 AM

Confirmations

6,582,251

Mined by

⛏️ P2SHASHCgr3FcMvAMVeUbxmte178wGe7VPFbY8

Merkle Root

9375d97e939b5d9f7db875949e764852c00d7d483beaffb47fde041662d48d34
Transactions (1)
Coinbase9375d97e939b5d…de041662d48d34
1 in β†’ 1 out10.1100 XPM109 B
ASHCgr3F…e7VPFbY8
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.

1.262 Γ— 10⁹²(93-digit number)
12622655652626718183…94852235002681371799
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
1.262 Γ— 10⁹²(93-digit number)
12622655652626718183…94852235002681371799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.262 Γ— 10⁹²(93-digit number)
12622655652626718183…94852235002681371801
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
2.524 Γ— 10⁹²(93-digit number)
25245311305253436366…89704470005362743599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.524 Γ— 10⁹²(93-digit number)
25245311305253436366…89704470005362743601
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
5.049 Γ— 10⁹²(93-digit number)
50490622610506872733…79408940010725487199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.049 Γ— 10⁹²(93-digit number)
50490622610506872733…79408940010725487201
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
1.009 Γ— 10⁹³(94-digit number)
10098124522101374546…58817880021450974399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.009 Γ— 10⁹³(94-digit number)
10098124522101374546…58817880021450974401
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
2.019 Γ— 10⁹³(94-digit number)
20196249044202749093…17635760042901948799
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:57,690,582 XPMΒ·at block #6,805,811 Β· updates every 60s
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