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Block #2,704,355

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/14/2018, 12:08:17 AM Β· Difficulty 11.6279 Β· 4,140,082 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4fc0720b371d9eadbaf8041379acf0149ea7f8752d4fe890380966acdae899f5
View on Chainz β†—

Height

#2,704,355

Difficulty

11.627921

Transactions

1

Size

201 B

Version

2

Bits

0ba0bf70

Nonce

1,086,647,905

Timestamp

6/14/2018, 12:08:17 AM

Confirmations

4,140,082

Mined by

⛏️ P2SHAag6fJmp7D2yK6LSa7fCMXPuBhu1k7t1kj

Merkle Root

2d5ec196115367b27aae642882f1b2053999181704a475b943a831d3aeb5a352
Transactions (1)
Coinbase2d5ec196115367…a831d3aeb5a352
1 in β†’ 1 out7.3800 XPM110 B
Aag6fJmp…u1k7t1kj
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.

2.316 Γ— 10⁹⁢(97-digit number)
23163073793090268790…19585986916157438719
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
2.316 Γ— 10⁹⁢(97-digit number)
23163073793090268790…19585986916157438719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.316 Γ— 10⁹⁢(97-digit number)
23163073793090268790…19585986916157438721
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
4.632 Γ— 10⁹⁢(97-digit number)
46326147586180537580…39171973832314877439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.632 Γ— 10⁹⁢(97-digit number)
46326147586180537580…39171973832314877441
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
9.265 Γ— 10⁹⁢(97-digit number)
92652295172361075160…78343947664629754879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.265 Γ— 10⁹⁢(97-digit number)
92652295172361075160…78343947664629754881
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
1.853 Γ— 10⁹⁷(98-digit number)
18530459034472215032…56687895329259509759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.853 Γ— 10⁹⁷(98-digit number)
18530459034472215032…56687895329259509761
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
3.706 Γ— 10⁹⁷(98-digit number)
37060918068944430064…13375790658519019519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.706 Γ— 10⁹⁷(98-digit number)
37060918068944430064…13375790658519019521
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
7.412 Γ— 10⁹⁷(98-digit number)
74121836137888860128…26751581317038039039
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:57,999,892 XPMΒ·at block #6,844,436 Β· updates every 60s
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