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Block #554,216

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/20/2014, 4:34:57 PM Β· Difficulty 10.9631 Β· 6,255,579 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
31f63190a04a9a59c9769155b14ef549d9d0ff1675eb2d1f795c2faa1711437c
View on Chainz β†—

Height

#554,216

Difficulty

10.963095

Transactions

1

Size

243 B

Version

2

Bits

0af68d68

Nonce

1,945,648,872

Timestamp

5/20/2014, 4:34:57 PM

Confirmations

6,255,579

Mined by

⛏️ P2SHARzmpY4cAhz8WiJkMBTqRELns6fvx8bF9t

Merkle Root

d45e454f663110b759c00134c3eef2b2bf279a4ea4f541cfe46cb43e0ed2a8de
Transactions (1)
Coinbased45e454f663110…6cb43e0ed2a8de
1 in β†’ 2 out8.3100 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.

9.134 Γ— 10⁹⁷(98-digit number)
91345693347716875561…45804474529087954399
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
9.134 Γ— 10⁹⁷(98-digit number)
91345693347716875561…45804474529087954399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.134 Γ— 10⁹⁷(98-digit number)
91345693347716875561…45804474529087954401
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
1.826 Γ— 10⁹⁸(99-digit number)
18269138669543375112…91608949058175908799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.826 Γ— 10⁹⁸(99-digit number)
18269138669543375112…91608949058175908801
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
3.653 Γ— 10⁹⁸(99-digit number)
36538277339086750224…83217898116351817599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.653 Γ— 10⁹⁸(99-digit number)
36538277339086750224…83217898116351817601
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
7.307 Γ— 10⁹⁸(99-digit number)
73076554678173500449…66435796232703635199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.307 Γ— 10⁹⁸(99-digit number)
73076554678173500449…66435796232703635201
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
1.461 Γ— 10⁹⁹(100-digit number)
14615310935634700089…32871592465407270399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.461 Γ— 10⁹⁹(100-digit number)
14615310935634700089…32871592465407270401
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
2.923 Γ— 10⁹⁹(100-digit number)
29230621871269400179…65743184930814540799
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:57,722,440 XPMΒ·at block #6,809,794 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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