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Block #547,726

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/16/2014, 3:38:55 PM Β· Difficulty 10.9576 Β· 6,264,409 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
18b898c87334b5b34053bf82b31b7f712ac16819194729e52c49e26fbf172b08
View on Chainz β†—

Height

#547,726

Difficulty

10.957596

Transactions

1

Size

243 B

Version

2

Bits

0af524fb

Nonce

101,067,173

Timestamp

5/16/2014, 3:38:55 PM

Confirmations

6,264,409

Mined by

⛏️ P2SHARzmpY4cAhz8WiJkMBTqRELns6fvx8bF9t

Merkle Root

9ee4063dba9e8703eb972404d98a10ed609ffa0e233641150c3b10646de1e66f
Transactions (1)
Coinbase9ee4063dba9e87…3b10646de1e66f
1 in β†’ 2 out8.3200 XPM152 B
ARzmpY4c…fvx8bF9tALPu3s2c…EJXLjVFh
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.

1.734 Γ— 10⁹⁸(99-digit number)
17341530326346565049…36717243386610104159
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
1.734 Γ— 10⁹⁸(99-digit number)
17341530326346565049…36717243386610104159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.734 Γ— 10⁹⁸(99-digit number)
17341530326346565049…36717243386610104161
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
3.468 Γ— 10⁹⁸(99-digit number)
34683060652693130098…73434486773220208319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.468 Γ— 10⁹⁸(99-digit number)
34683060652693130098…73434486773220208321
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
6.936 Γ— 10⁹⁸(99-digit number)
69366121305386260196…46868973546440416639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.936 Γ— 10⁹⁸(99-digit number)
69366121305386260196…46868973546440416641
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
1.387 Γ— 10⁹⁹(100-digit number)
13873224261077252039…93737947092880833279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.387 Γ— 10⁹⁹(100-digit number)
13873224261077252039…93737947092880833281
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
2.774 Γ— 10⁹⁹(100-digit number)
27746448522154504078…87475894185761666559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.774 Γ— 10⁹⁹(100-digit number)
27746448522154504078…87475894185761666561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,741,094 XPMΒ·at block #6,812,134 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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