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Block #2,169,419

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/20/2017, 9:56:47 PM Β· Difficulty 10.8997 Β· 4,671,321 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
23a69727f22a4139a74808b0ab25ae35e13373ede089baf705f8c31f6d1c14e8
View on Chainz β†—

Height

#2,169,419

Difficulty

10.899701

Transactions

2

Size

8.95 KB

Version

2

Bits

0ae652cb

Nonce

121,782,582

Timestamp

6/20/2017, 9:56:47 PM

Confirmations

4,671,321

Mined by

⛏️ P2SHAReuF48Gu1qWo5qdMsuN1HJ5R9A96N9RgV

Merkle Root

42de5bf8672671921752aa41641481779607a83ef8c79396574ae5b7a85b3a09
Transactions (2)
Coinbaseedfc014aba47a2…bbf2bed80cae91
1 in β†’ 1 out8.5100 XPM109 B
AReuF48G…A96N9RgV
e7639384fcab26…e05a5dc9747719
60 in β†’ 2 out1359.4697 XPM8.75 KB
Ada1dx2w…8gd1gZg2AV4Z6vEo…npBnBjnK
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.

5.941 Γ— 10⁹⁷(98-digit number)
59418542473072976752…25166937968437329919
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
5.941 Γ— 10⁹⁷(98-digit number)
59418542473072976752…25166937968437329919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.941 Γ— 10⁹⁷(98-digit number)
59418542473072976752…25166937968437329921
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
1.188 Γ— 10⁹⁸(99-digit number)
11883708494614595350…50333875936874659839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.188 Γ— 10⁹⁸(99-digit number)
11883708494614595350…50333875936874659841
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
2.376 Γ— 10⁹⁸(99-digit number)
23767416989229190701…00667751873749319679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.376 Γ— 10⁹⁸(99-digit number)
23767416989229190701…00667751873749319681
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
4.753 Γ— 10⁹⁸(99-digit number)
47534833978458381402…01335503747498639359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.753 Γ— 10⁹⁸(99-digit number)
47534833978458381402…01335503747498639361
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
9.506 Γ— 10⁹⁸(99-digit number)
95069667956916762804…02671007494997278719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.506 Γ— 10⁹⁸(99-digit number)
95069667956916762804…02671007494997278721
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
1.901 Γ— 10⁹⁹(100-digit number)
19013933591383352560…05342014989994557439
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:57,970,263 XPMΒ·at block #6,840,739 Β· updates every 60s
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