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Block #217,963

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/19/2013, 3:59:54 PM Β· Difficulty 9.9294 Β· 6,608,433 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4710a952345535c87fdf11431f736e24cad95fc703dc9b4cd0010887ff3a85f3
View on Chainz β†—

Height

#217,963

Difficulty

9.929374

Transactions

2

Size

2.15 KB

Version

2

Bits

09edeb79

Nonce

108,569

Timestamp

10/19/2013, 3:59:54 PM

Confirmations

6,608,433

Mined by

⛏️ P2SHAbGZZ5j9xYn1T2NM8sUHpoY2ocPsAgN9dv

Merkle Root

4b206df260a82b709e527c54399f2bd282d2e0304e1d0344f6db32c1788905b7
Transactions (2)
Coinbaseea5f8daf841f07…9eb8e86b83cf84
1 in β†’ 1 out10.1600 XPM109 B
AbGZZ5j9…PsAgN9dv
ec33284f2dcb08…7b729ac967b7e9
13 in β†’ 2 out135.5912 XPM1.95 KB
AN45xKJb…jzPnBV6LAXJqv4eu…SN1MN5Ry
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.

2.940 Γ— 10⁹³(94-digit number)
29403177738326450877…82155889551550087999
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
2.940 Γ— 10⁹³(94-digit number)
29403177738326450877…82155889551550087999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.940 Γ— 10⁹³(94-digit number)
29403177738326450877…82155889551550088001
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
5.880 Γ— 10⁹³(94-digit number)
58806355476652901755…64311779103100175999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.880 Γ— 10⁹³(94-digit number)
58806355476652901755…64311779103100176001
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
1.176 Γ— 10⁹⁴(95-digit number)
11761271095330580351…28623558206200351999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.176 Γ— 10⁹⁴(95-digit number)
11761271095330580351…28623558206200352001
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
2.352 Γ— 10⁹⁴(95-digit number)
23522542190661160702…57247116412400703999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.352 Γ— 10⁹⁴(95-digit number)
23522542190661160702…57247116412400704001
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
4.704 Γ— 10⁹⁴(95-digit number)
47045084381322321404…14494232824801407999
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:57,855,307 XPMΒ·at block #6,826,395 Β· updates every 60s
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