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Block #130,224

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/23/2013, 11:19:54 AM Β· Difficulty 9.7839 Β· 6,678,761 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ce2705acd930ee4287d6deeec354769462b4025dffde6743a7ecc9590b80faf8
View on Chainz β†—

Height

#130,224

Difficulty

9.783898

Transactions

2

Size

1018 B

Version

2

Bits

09c8ad91

Nonce

27,117

Timestamp

8/23/2013, 11:19:54 AM

Confirmations

6,678,761

Mined by

⛏️ P2SHAbowyc1u7HYh72pPFAMLqww8KD2vEJ15F9

Merkle Root

4bf76584c1dd64aa8e1da70c3e47fa6ec8b331ff880c7cc3ee9bfd1ec22ed14c
Transactions (2)
Coinbasef9f58e55b25e15…051c737bb4b762
1 in β†’ 1 out10.4400 XPM109 B
Abowyc1u…2vEJ15F9
a4af1da371b598…020351db417d1f
5 in β†’ 2 out6.0948 XPM818 B
ASp5LpEk…ysAXeaYeAZ92ewYE…YrLqpVUt
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.

2.718 Γ— 10⁹⁢(97-digit number)
27189719997362974208…95869472055999549969
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
2.718 Γ— 10⁹⁢(97-digit number)
27189719997362974208…95869472055999549969
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.718 Γ— 10⁹⁢(97-digit number)
27189719997362974208…95869472055999549971
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
5.437 Γ— 10⁹⁢(97-digit number)
54379439994725948416…91738944111999099939
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.437 Γ— 10⁹⁢(97-digit number)
54379439994725948416…91738944111999099941
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
1.087 Γ— 10⁹⁷(98-digit number)
10875887998945189683…83477888223998199879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.087 Γ— 10⁹⁷(98-digit number)
10875887998945189683…83477888223998199881
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
2.175 Γ— 10⁹⁷(98-digit number)
21751775997890379366…66955776447996399759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.175 Γ— 10⁹⁷(98-digit number)
21751775997890379366…66955776447996399761
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
4.350 Γ— 10⁹⁷(98-digit number)
43503551995780758733…33911552895992799519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.350 Γ— 10⁹⁷(98-digit number)
43503551995780758733…33911552895992799521
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:57,715,937 XPMΒ·at block #6,808,984 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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