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Block #2,702,966

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/13/2018, 12:16:34 AM Β· Difficulty 11.6310 Β· 4,138,385 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c67cef700bc8878a042fb72881b7a922951cd69be2a1870320b5e1a48c1c6d34
View on Chainz β†—

Height

#2,702,966

Difficulty

11.631023

Transactions

1

Size

200 B

Version

2

Bits

0ba18abf

Nonce

593,749,771

Timestamp

6/13/2018, 12:16:34 AM

Confirmations

4,138,385

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

9ddcb919108c38eaabeaf06539e9995a3dcbc29b80712afb0a9c989e92fd6f30
Transactions (1)
Coinbase9ddcb919108c38…9c989e92fd6f30
1 in β†’ 1 out7.3800 XPM109 B
AZtxQr2F…7grUWrUz
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.

5.720 Γ— 10⁹⁡(96-digit number)
57204826066794111994…72221087842626137599
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
5.720 Γ— 10⁹⁡(96-digit number)
57204826066794111994…72221087842626137599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.720 Γ— 10⁹⁡(96-digit number)
57204826066794111994…72221087842626137601
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
1.144 Γ— 10⁹⁢(97-digit number)
11440965213358822398…44442175685252275199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.144 Γ— 10⁹⁢(97-digit number)
11440965213358822398…44442175685252275201
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
2.288 Γ— 10⁹⁢(97-digit number)
22881930426717644797…88884351370504550399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.288 Γ— 10⁹⁢(97-digit number)
22881930426717644797…88884351370504550401
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
4.576 Γ— 10⁹⁢(97-digit number)
45763860853435289595…77768702741009100799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.576 Γ— 10⁹⁢(97-digit number)
45763860853435289595…77768702741009100801
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
9.152 Γ— 10⁹⁢(97-digit number)
91527721706870579190…55537405482018201599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.152 Γ— 10⁹⁢(97-digit number)
91527721706870579190…55537405482018201601
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
1.830 Γ— 10⁹⁷(98-digit number)
18305544341374115838…11074810964036403199
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:57,975,175 XPMΒ·at block #6,841,350 Β· updates every 60s
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