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Block #2,739,708

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/8/2018, 3:26:29 PM Β· Difficulty 11.6199 Β· 4,099,644 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
16a3248b7d9a649bdf281b7b530f16924189d2b0c65eb0fac9c1f064c5c79ca6
View on Chainz β†—

Height

#2,739,708

Difficulty

11.619935

Transactions

2

Size

3.29 KB

Version

2

Bits

0b9eb40c

Nonce

934,296,032

Timestamp

7/8/2018, 3:26:29 PM

Confirmations

4,099,644

Mined by

⛏️ P2SHAHY2GaipfTMz4phVGxWTLYMeM3M1ZxTsF5

Merkle Root

9fce2b79894bec053f004bd676c3d336b87f723c089861e8a1166af0ffed94db
Transactions (2)
Coinbase272eb18027383a…30e664331bfb47
1 in β†’ 1 out7.4300 XPM110 B
AHY2Gaip…M1ZxTsF5
548d60abef2308…15982f69ad0419
21 in β†’ 2 out250.0135 XPM3.10 KB
AKDgdZsc…N8Chkw1CAJcDB81D…ZX2on3Cs
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.

1.786 Γ— 10⁹⁴(95-digit number)
17864161408079614637…63324076625333450239
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
1.786 Γ— 10⁹⁴(95-digit number)
17864161408079614637…63324076625333450239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.786 Γ— 10⁹⁴(95-digit number)
17864161408079614637…63324076625333450241
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
3.572 Γ— 10⁹⁴(95-digit number)
35728322816159229275…26648153250666900479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.572 Γ— 10⁹⁴(95-digit number)
35728322816159229275…26648153250666900481
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
7.145 Γ— 10⁹⁴(95-digit number)
71456645632318458550…53296306501333800959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.145 Γ— 10⁹⁴(95-digit number)
71456645632318458550…53296306501333800961
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
1.429 Γ— 10⁹⁡(96-digit number)
14291329126463691710…06592613002667601919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.429 Γ— 10⁹⁡(96-digit number)
14291329126463691710…06592613002667601921
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
2.858 Γ— 10⁹⁡(96-digit number)
28582658252927383420…13185226005335203839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.858 Γ— 10⁹⁡(96-digit number)
28582658252927383420…13185226005335203841
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
5.716 Γ— 10⁹⁡(96-digit number)
57165316505854766840…26370452010670407679
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:57,959,102 XPMΒ·at block #6,839,351 Β· updates every 60s
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