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Block #3,181,556

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/14/2019, 9:10:46 AM Β· Difficulty 11.2589 Β· 3,659,911 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
80383d8a0a863b767261e88ebc43ece7b1681cc16306aa1bea3562559765c87d
View on Chainz β†—

Height

#3,181,556

Difficulty

11.258850

Transactions

1

Size

201 B

Version

2

Bits

0b424400

Nonce

1,767,455,472

Timestamp

5/14/2019, 9:10:46 AM

Confirmations

3,659,911

Mined by

⛏️ P2SHARbm48qRsZyALB7gqdgsMMKGGA9xQc8DBX

Merkle Root

ca786a024a04f56daaf94c23e959e4ea47ff24cd29aabdb05d893cede3732cfb
Transactions (1)
Coinbaseca786a024a04f5…893cede3732cfb
1 in β†’ 1 out7.8800 XPM110 B
ARbm48qR…9xQc8DBX
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.

3.290 Γ— 10⁹⁷(98-digit number)
32901675771144381168…77906320430882815999
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
3.290 Γ— 10⁹⁷(98-digit number)
32901675771144381168…77906320430882815999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.290 Γ— 10⁹⁷(98-digit number)
32901675771144381168…77906320430882816001
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
6.580 Γ— 10⁹⁷(98-digit number)
65803351542288762336…55812640861765631999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.580 Γ— 10⁹⁷(98-digit number)
65803351542288762336…55812640861765632001
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
1.316 Γ— 10⁹⁸(99-digit number)
13160670308457752467…11625281723531263999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.316 Γ— 10⁹⁸(99-digit number)
13160670308457752467…11625281723531264001
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
2.632 Γ— 10⁹⁸(99-digit number)
26321340616915504934…23250563447062527999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.632 Γ— 10⁹⁸(99-digit number)
26321340616915504934…23250563447062528001
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
5.264 Γ— 10⁹⁸(99-digit number)
52642681233831009869…46501126894125055999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.264 Γ— 10⁹⁸(99-digit number)
52642681233831009869…46501126894125056001
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
1.052 Γ— 10⁹⁹(100-digit number)
10528536246766201973…93002253788250111999
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:57,976,110 XPMΒ·at block #6,841,466 Β· updates every 60s
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