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Block #154,242

TWNLength 9ā˜…ā˜†ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 9/7/2013, 1:01:48 PM Ā· Difficulty 9.8644 Ā· 6,640,807 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3d1e75d66327dd5d6c2fb40318481abb5a98efbd32439ef770c3a60a64423a72
View on Chainz ā†—

Height

#154,242

Difficulty

9.864371

Transactions

4

Size

990 B

Version

2

Bits

09dd476d

Nonce

201,183

Timestamp

9/7/2013, 1:01:48 PM

Confirmations

6,640,807

Mined by

ā›ļø P2SHARnh8fyjfqLyTBAcZ6LAfN3cugjtwuU1UT

Merkle Root

e06019e8fe0034f5425ae1a41912661204ade1060c266687245c9982d4d29682
Transactions (4)
Coinbasecce193b4d278b8ā€¦a289bd39316e57
1 in ā†’ 1 out10.2900 XPM109 B
ARnh8fyjā€¦jtwuU1UT
e0e304fd2c08feā€¦4a50afb0908184
2 in ā†’ 1 out4.0236 XPM339 B
AZekc9vMā€¦TkyD7EeC
e589d03e52eb12ā€¦2e56c94cf0bf94
1 in ā†’ 2 out8.2246 XPM226 B
Ad6kxrcwā€¦74KCVPR3AcN7Mwejā€¦Rnr1man2
9ae87db8084f16ā€¦b8e0f70d694be8
1 in ā†’ 2 out6.2376 XPM226 B
AJv5WoqTā€¦tqCRQqFkAUwcT5AXā€¦vRPRVx5D
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) ā€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.975 Ɨ 10ā¹āµ(96-digit number)
29756708831968499659ā€¦68225442954879395099
Discovered Prime Numbers
Lower: 2^k Ɨ origin āˆ’ 1 | Upper: 2^k Ɨ 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 ā€” Twin Prime Pair (origin Ā± 1)
origin āˆ’ 1
2.975 Ɨ 10ā¹āµ(96-digit number)
29756708831968499659ā€¦68225442954879395099
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
2.975 Ɨ 10ā¹āµ(96-digit number)
29756708831968499659ā€¦68225442954879395101
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: origin + 1 āˆ’ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 1 ā€” Twin Prime Pair (2^1 Ɨ origin Ā± 1)
2^1 Ɨ origin āˆ’ 1
5.951 Ɨ 10ā¹āµ(96-digit number)
59513417663936999319ā€¦36450885909758790199
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
5.951 Ɨ 10ā¹āµ(96-digit number)
59513417663936999319ā€¦36450885909758790201
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^1 Ɨ origin + 1 āˆ’ 2^1 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 2 ā€” Twin Prime Pair (2^2 Ɨ origin Ā± 1)
2^2 Ɨ origin āˆ’ 1
1.190 Ɨ 10ā¹ā¶(97-digit number)
11902683532787399863ā€¦72901771819517580399
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
1.190 Ɨ 10ā¹ā¶(97-digit number)
11902683532787399863ā€¦72901771819517580401
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^2 Ɨ origin + 1 āˆ’ 2^2 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 3 ā€” Twin Prime Pair (2^3 Ɨ origin Ā± 1)
2^3 Ɨ origin āˆ’ 1
2.380 Ɨ 10ā¹ā¶(97-digit number)
23805367065574799727ā€¦45803543639035160799
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
2.380 Ɨ 10ā¹ā¶(97-digit number)
23805367065574799727ā€¦45803543639035160801
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^3 Ɨ origin + 1 āˆ’ 2^3 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 4 ā€” Twin Prime Pair (2^4 Ɨ origin Ā± 1)
2^4 Ɨ origin āˆ’ 1
4.761 Ɨ 10ā¹ā¶(97-digit number)
47610734131149599455ā€¦91607087278070321599
Verify on FactorDB ā†—Wolfram Alpha ā†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin ā€” the large number shown above ā€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

ā˜…ā˜†ā˜†ā˜†ā˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 Ɨ 3 Ɨ 5 Ɨ 7 Ɨ ā€¦), the result is the first prime in the chain. The origin is deliberately divisible by this primorial ā€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Ɨ Primorial (2Ā·3Ā·5Ā·7Ā·11Ā·ā€¦)
Source: Primecoin prime.cpp ā€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors ā€” 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 āˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,604,432 XPMĀ·at block #6,795,048 Ā· updates every 60s
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