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Block #488,587

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/12/2014, 6:57:39 PM Β· Difficulty 10.6575 Β· 6,318,642 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cf97f2d9d6fa935f0b6a032c00f92be14e31b8e315afbeee4d90d322daf39368
View on Chainz β†—

Height

#488,587

Difficulty

10.657514

Transactions

1

Size

207 B

Version

2

Bits

0aa852da

Nonce

336,848,950

Timestamp

4/12/2014, 6:57:39 PM

Confirmations

6,318,642

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

cc1f7db257b4541ba7b02c6cba1499142d816f18ebd31ac3d562940deb3a8516
Transactions (1)
Coinbasecc1f7db257b454…62940deb3a8516
1 in β†’ 1 out8.7900 XPM116 B
AbwWkWZt…kawDhufa
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.

1.180 Γ— 10⁹⁸(99-digit number)
11808182655060235992…70726069934554373999
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
1.180 Γ— 10⁹⁸(99-digit number)
11808182655060235992…70726069934554373999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.180 Γ— 10⁹⁸(99-digit number)
11808182655060235992…70726069934554374001
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
2.361 Γ— 10⁹⁸(99-digit number)
23616365310120471985…41452139869108747999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.361 Γ— 10⁹⁸(99-digit number)
23616365310120471985…41452139869108748001
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
4.723 Γ— 10⁹⁸(99-digit number)
47232730620240943970…82904279738217495999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.723 Γ— 10⁹⁸(99-digit number)
47232730620240943970…82904279738217496001
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
9.446 Γ— 10⁹⁸(99-digit number)
94465461240481887940…65808559476434991999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.446 Γ— 10⁹⁸(99-digit number)
94465461240481887940…65808559476434992001
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
1.889 Γ— 10⁹⁹(100-digit number)
18893092248096377588…31617118952869983999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.889 Γ— 10⁹⁹(100-digit number)
18893092248096377588…31617118952869984001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
3.778 Γ— 10⁹⁹(100-digit number)
37786184496192755176…63234237905739967999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,701,848 XPMΒ·at block #6,807,228 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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